Solve the absolute value inequality. 25x < or equal to 0. (2 minus 5x is less than or equal to 0)
 print Print
 list Cite
5 Answers
 2  5x  <= 0
the absolute value is always positive. Therefore, it is never less than zero. It can, however, be equal to zero:
2  5x = 0
x = 2/5
To solve 25x < = 0
Solution:
If 25x is < 0 then 25x = 5x2 by definition . So 5x2 < 0 by definition.
It is a contradiction
If 25x > 0, then 25x =25x by definition. So 25x < 0 a contradiction.
So x > 2/5.
2 < 5x, x >2/5.
So x cannot be greater than 2/5 and x cannot be less than 2/5.
Therefore x = 2/5 is the only value that satisfies 25x < = 0.

25x < or equal to 0
the l l makes the numbers positive so:
2 + 5x < or equal to 0
now move the 5x
2 `<=` 5x
divide by 5
`2/5 >= x`
now change the sign since you divided:
`2/5 lt=` `x`
25x < or equal to 0.
so 25x< or equal to 0
Move the 5x on the other side so the equation stays positive
2<5x
then simply divide by 5 to isolate the variable (x)
x>2/5
The sign changed because you divided by 5, once you divide it changes the sign
So the answer is x>2/5
Thank you so much!